Enlarging the Options in the Strategy-based Transit Assignment TRB Applications Conference Reno 2011 Isabelle Constantin and Michael Florian INRO

TRB Applications Conference Reno 2011 Motivation Computing logit choice of strategies Distribution of flow between connectors Distribution of flow between attractive lines Conclusions Contents

TRB Applications Conference Reno 2011 Strategy-based Transit Assignment The optimal strategy algorithm is well understood and field tested Extended successfully to congested transit assignment and capacitated transit assignment Further extensions can provide a richer set of transit modeling features

TRB Applications Conference Reno 2011 Deterministic vs Stochastic Strategies Currently in an optimal strategy All the flow at a node either 1. leaves by the best walk link, or 2. waits at the node for the first attractive line to be served Logit choice of strategies A logit model can be used to distribute the flow at a node between ride and walk options: 1. leaving by the best walk link or other “efficient” walk links 2. waiting at the node for the first “efficient” line to be served

TRB Applications Conference Reno 2011 Adding a Walk-to-line Option: a Small Example 12 min 30 min 6 min Headway 4 min 7 min 25 minutes 6 min 10 min 4 min O A D B Line The demand from O to D is 100

TRB Applications Conference Reno 2011 The Optimal Strategy 12 min 30 min 6 min Headway 50 trips trips 8.33 trips O A D B Expected travel time min Line

TRB Applications Conference Reno 2011 Adding a Walk-to-transit Option 4 min 7 min 25 minutes 6 min 15 min 4 min O A D B E 6 min 10 min New walk path is 26 min 12 min 30 min 6 min 10 min HeadwayLine

6 min TRB Applications Conference Reno 2011 Adding a Walk-to-transit Option 4 min 7 min 25 minutes 6 min 15 min 4 min O A D B E 10 min First strategy time is min 12 min 30 min 6 min 10 min HeadwayLine

TRB Applications Conference Reno 2011 Adding a Walk-to-transit Option 4 min 7 min 25 minutes 6 min 15 min 4 min O A D B E 6 min 10 min Second strategy time is min 12 min 30 min 6 min 10 min HeadwayLine

TRB Applications Conference Reno 2011 Adding a Walk-to-transit Option 4 min 7 min 25 minutes 6 min 15 min 4 min O A D B E 6 min 10 min New walk path is 26 min (vs min) Optimal strategy is to walk to the orange line 12 min 30 min 6 min 10 min HeadwayLine

Logit Choice of Strategies 12 min 30 min 6 min 10 min Headway 22.9 trips 54.2 trips trips O A D B Line E 3.82 trips TRB Applications Conference Reno 2011 Logit choice of strategies (with scale = 0.1) First strategy 45.8 trips Second strategy54.2 trips

TRB Applications Conference Reno 2011 Adding a Walk-to-transit Option 4 min 7 min 25 minutes 6 min 17 min 4 min O A D B E 6 min 10 min The travel time of the orange line is increased by 2 minutes to 17 minutes 12 min 30 min 6 min 10 min HeadwayLine

TRB Applications Conference Reno 2011 Logit Choice of Strategies 4 min 7 min 25 minutes 6 min 17 min 4 min O A D B E 6 min 10 min Second strategy time is now min 12 min 30 min 6 min 10 min HeadwayLine

TRB Applications Conference Reno 2011 Adding a Walk-to-transit Option 4 min 7 min 25 minutes 6 min 17 min 4 min O A D B E 6 min 10 min New walk path is 28 min vs min Optimal strategy does not use the walk to the orange line 12 min 30 min 6 min 10 min HeadwayLine

TRB Applications Conference Reno 2011 Logit Choice of Strategies O A D B E 12 min 30 min 6 min 10 min HeadwayLine Logit choice of strategies (with scale = 0.1) First strategy trips Second strategy trips 25.3 trips 49.4 trips 21.1 trips 4.2 trips

TRB Applications Conference Reno 2011 Motivation Computing logit choice of strategies Distribution of flow between connectors Distribution of flow between attractive lines Conclusions Contents

TRB Applications Conference Reno 2011 Option 1 Generate a set of paths by O-D pair prior to the execution of the route choice algorithm Drawbacks  the paths are generated by using heuristics, so the path choices are somewhat arbitrary  the paths are processed by O-D pair, so the computation time increases as the square of the number of zones How Can One Enlarge the Choice Set?

TRB Applications Conference Reno 2011 Option 2 Enlarge the set of walk links and transit line segments that are considered in the transit assignment by using a well defined criterion Advantage  This preserves the computations by destination, so the computation time increases only linearly with the number of zones This is the approach that we have chosen How Can One Enlarge the Choice Set?

TRB Applications Conference Reno 2011 The optimal strategy algorithm is first modified to compute simultaneously at each node two values: The best expected travel and wait times from a node to the destination either:  by boarding a vehicle at the node, and  by walking to another node(stop) to board a vehicle. Modified Strategy Computation

TRB Applications Conference Reno 2011 Then, any “efficient arcs” or “efficient line segments" are included, in addition to those of the optimal strategy, by using the criteria:  a walk arc is efficient if, by taking it, one gets nearer to the destination  a transit segment is efficient if, by boarding it, the best alighting stop is nearer to the destination Node likelihoods are computed recursively in order to obtain the probabilities (proportions) of all the strategies included Modified Strategy Computation

Another Example TRB Applications Conference Reno 2011 The demand is 100 in each direction

TRB Applications Conference Reno 2011 Another Example: Optimal Strategy

TRB Applications Conference Reno 2011 Scale: 0.2 Logit Choice of Strategies

TRB Applications Conference Reno 2011 There is another way to ensure that more than one connector is used to access the transit services:  Apply the logit choice only to the connectors by considering the length of each connector and the expected travel time to destination from the accessed node Distribution of Flow Between Connectors

TRB Applications Conference Reno 2011 Scale: 0.2 Cut-off: 0.01 Logit Choice Only on Connectors

TRB Applications Conference Reno 2011 Another Example: Optimal Strategy

TRB Applications Conference Reno 2011 Optimal strategy when eastbound tram time is increased Distribution of Flow – Increased Tram Time

TRB Applications Conference Reno 2011 Logit on strategies when tram ride time is increased Distribution of Flow – Increased Tram Time

TRB Applications Conference Reno 2011 Logit choice only on connectors Distribution of Flow – Increased Tram Time

TRB Applications Conference Reno 2011 The issues that are addressed Computing logit choice of strategies Distribution of flow between connectors Distribution of flow between attractive lines Conclusions Contents

TRB Applications Conference Reno 2011 Optimal strategy assignment: the flow at a transit node is distributed based on frequency p l = f l / f where f = sum of the frequency of the attractive lines Suboptimal strategy taking into account line travel times: the flow at a transit node can also be distributed based on frequency and time to destination by giving priority to the faster lines p l = p_adjust l * f l / f where the adjustment factor is computed as and the fastest line is considered first Distribution of Flow Between Attractive Lines

TRB Applications Conference Reno 2011 Optimal Strategy Distribution of Flow Between Attractive Lines

TRB Applications Conference Reno 2011 Logit choice of strategies and transit time to destination Distribution of Flow Between Attractive Lines

TRB Applications Conference Reno 2011 Motivation Logit choice of strategies Distribution of flow between connectors Distribution of flow between attractive lines Conclusions Contents

TRB Applications Conference Reno 2011 The consideration of a richer set of strategies Inclusion of walk in “sub-optimal” strategies Modeling of uneven population distribution in large zones Evaluation measures based on log-sum computations Without losing any computational efficiency … Enhanced modeling possibilities